butools.mam.QBDStationaryDistr¶

butools.mam.QBDStationaryDistr()¶

Matlab:	pi = QBDStationaryDistr (pi0, R, K)
Mathematica:	pi = QBDStationaryDistr [pi0, R, K]
Python/Numpy:	pi = QBDStationaryDistr (pi0, R, K)

Returns the stationary distribution of a QBD up to a given level K.

Parameters:	pi0 : matrix, shape (1,N) The stationary probability vector of level zero R : matrix, shape (N,N) The matrix parameter of the matrix geometrical distribution of the QBD K : integer The stationary distribution is returned up to this level.
Returns:	pi : array, length (K+1)*N The stationary probability vector up to level K

Examples

For Matlab:

>>> B = [0., 0.; 3., 4.];
>>> L = [-6., 5.; 3., -12.];
>>> F = [1., 0.; 2., 0.];
>>> L0 = [-6., 5.; 6., -8.];
>>> pi = QBDStationaryDistr(pi0, R, 5);
>>> disp(pi);
  Columns 1 through 6
      0.22992      0.18681      0.16802     0.086221     0.094781     0.048638
  Columns 7 through 12
     0.053466     0.027437     0.030161     0.015477     0.017014    0.0087307

For Mathematica:

>>> B = {{0., 0.},{3., 4.}};
>>> L = {{-6., 5.},{3., -12.}};
>>> F = {{1., 0.},{2., 0.}};
>>> L0 = {{-6., 5.},{6., -8.}};
>>> pi = QBDStationaryDistr[pi0, R, 5];
>>> Print[pi];
{0.22992392223161465, 0.18681318681318687, 0.1680213277846414, 0.08622147083685547, 0.09478126182723359, 0.048637752779764606, 0.05346635282561894, 0.02743668105525182, 0.03016050672214401, 0.015477102133731794, 0.017013619176594053, 0.00873067299851537}

For Python/Numpy:

>>> B = ml.matrix([[0., 0.],[3., 4.]])
>>> L = ml.matrix([[-6., 5.],[3., -12.]])
>>> F = ml.matrix([[1., 0.],[2., 0.]])
>>> L0 = ml.matrix([[-6., 5.],[6., -8.]])
>>> pi = QBDStationaryDistr(pi0, R, 5)
>>> print(pi)
[[ 0.22992  0.18681  0.16802  0.08622  0.09478  0.04864  0.05347  0.02744  0.03016  0.01548  0.01701  0.00873]]